A Non-probabilistic Reliability-based Optimization of Structures Using Convex Models

摘要

This paper aims to propose a non-probabilistic reliability-based multi-objective optimization method for structures with uncertain-but-bounded parameters. A combination of the interval and ellipsoid convex models is used to account for the different groups of uncertain parameters, in which the interval model accounts for uncorrelated parameters, while the ellipsoid model is applied to correlated parameters. The design is then formulated as a nested double-loop optimization problem. A multi-objective genetic algorithm is used in the out loop optimization to optimize the design vector for evaluating the objectives, and the Sequential Quadratic Programming (SQP) algorithm is applied in the inner loop to evaluate the uncertain vector and non-probabilistic reliability index. Since the double-loop process for most engineering problems is computationally prohibitive, the polynomial response surface method (RSM) is applied to construct a surrogate model for the approximation of the objective functions and constraints, in order to improve the computational efficiency. In this way, a new reliability-based optimization method is established as a nature combination of the non-probabilistic multi-objective optimization method using convex models with the surrogate model. Typical numerical examples and a practical engineering application are used to demonstrate the effectiveness of the proposed optimization method.